.. _runs-mock:

Uchuu Mock VLIM M★ — Run Summary
==================================

Uchuu N-body mock catalogues are matched to the BGS VLIM M★ samples
by density, redshift range, and stellar-mass threshold.
The summary statistics are computed with ``measure_MOCK_VLIM_Mstar.ipynb``.

**Cosmology:** Planck18 (H₀ = 67.4, Ω_m = 0.315)

**Survey footprint:** 1/8 sky, RA ∈ [180°, 270°], Dec ∈ [−90°, 0°],
area = **5 156.6 deg²**.

**Redshift column:** ``redshift_S`` (spectroscopic-like).
**Stellar mass column:** ``log₁₀(obs_sm)`` (SHAM-assigned masses).
**Weights:** uniform (no systematic correction).

.. note::
   All samples use 100 jackknife regions (``N_JK=100``).
   Random catalogues are subsampled to 5 × N_gal before pair counting
   to keep corrfunc tree overhead manageable for small-volume samples.

Sample inventory
----------------

.. list-table::
   :header-rows: 1
   :widths: 30 12 10 10 12 10

   * - Sample key
     - N_gal
     - z_min
     - z_max
     - log₁₀M★_min
     - N_JK
   * - MOCK_VLIM_ANY_Mstar9.29_z0.05-0.08
     - 155 846
     - 0.05
     - 0.08
     - 9.29
     - 100
   * - MOCK_VLIM_ANY_Mstar9.78_z0.05-0.12
     - 408 958
     - 0.05
     - 0.12
     - 9.78
     - 100
   * - MOCK_VLIM_ANY_Mstar10.24_z0.05-0.18
     - 781 950
     - 0.05
     - 0.18
     - 10.24
     - 100
   * - MOCK_VLIM_ANY_Mstar10.45_z0.05-0.22
     - 936 461
     - 0.05
     - 0.22
     - 10.45
     - 100
   * - MOCK_VLIM_ANY_Mstar10.65_z0.05-0.26
     - 923 373
     - 0.05
     - 0.26
     - 10.65
     - 100
   * - MOCK_VLIM_ANY_Mstar10.84_z0.05-0.31
     - 793 669
     - 0.05
     - 0.31
     - 10.84
     - 100
   * - MOCK_VLIM_ANY_Mstar11.03_z0.05-0.35
     - 460 808
     - 0.05
     - 0.35
     - 11.03
     - 100
   * - MOCK_VLIM_ANY_Mstar11.22_z0.05-0.35
     - 157 946
     - 0.05
     - 0.35
     - 11.22
     - 100
   * - MOCK_VLIM_ANY_Mstar11.39_z0.05-0.35
     - 50 067
     - 0.05
     - 0.35
     - 11.39
     - 100

Output files
------------

.. code-block:: text

   data/mocks/
   ├── twopcf/{key}-wtheta.h5          w(θ)   — Landy–Szalay, TreeCorr variance
   ├── twopcf/{key}-wp-pimax100.h5     wp(rp) — Landy–Szalay, TreeCorr variance
   ├── lf_smf/{key}-smf-vmax.h5        SMF    — 1/Vmax, jackknife covariance
   └── joint/{key}-joint_smf_wp.h5     Joint SMF + wp, full jackknife covariance

Sample characterisation
------------------------

Figures below are produced by ``make_mocks`` and show the match between
the BGS observation (blue) and the Uchuu mock (orange).  All 9 samples
are now characterised.

M★ ≥ 9.29 (N = 155 846, z < 0.08)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. figure:: ../figures/runs/MOCK_VLIM_ANY_9.29_Mstar_12.0_0.05_z_0.08_N_0155846_compare_sky.png
   :width: 90%
   :alt: Sky footprint of mock M*≥9.29

   Sky footprint (RA/Dec) of the M★≥9.29 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_9.29_Mstar_12.0_0.05_z_0.08_N_0155846_compare_1D.png
   :width: 90%
   :alt: Redshift and mass distributions M*≥9.29

   Redshift (left) and stellar-mass (right) distributions for the M★≥9.29 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_9.29_Mstar_12.0_0.05_z_0.08_N_0155846_compare_zMstar.png
   :width: 90%
   :alt: z-M* plane M*≥9.29

   Stellar-mass vs. redshift plane for the M★≥9.29 mock and the corresponding BGS sample.

M★ ≥ 9.78 (N = 408 958, z < 0.12)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. figure:: ../figures/runs/MOCK_VLIM_ANY_9.78_Mstar_12.0_0.05_z_0.12_N_0408958_compare_sky.png
   :width: 90%
   :alt: Sky footprint of mock M*≥9.78

   Sky footprint (RA/Dec) of the M★≥9.78 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_9.78_Mstar_12.0_0.05_z_0.12_N_0408958_compare_1D.png
   :width: 90%
   :alt: Redshift and mass distributions M*≥9.78

   Redshift (left) and stellar-mass (right) distributions for the M★≥9.78 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_9.78_Mstar_12.0_0.05_z_0.12_N_0408958_compare_zMstar.png
   :width: 90%
   :alt: z-M* plane M*≥9.78

   Stellar-mass vs. redshift plane for the M★≥9.78 mock and the corresponding BGS sample.

M★ ≥ 10.24 (N = 781 950, z < 0.18)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.24_Mstar_12.0_0.05_z_0.18_N_0781950_compare_sky.png
   :width: 90%
   :alt: Sky footprint of mock M*≥10.24

   Sky footprint (RA/Dec) of the M★≥10.24 mock.  The mock covers the
   southern Galactic octant (RA ∈ [180°, 270°], Dec < 0°).

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.24_Mstar_12.0_0.05_z_0.18_N_0781950_compare_1D.png
   :width: 90%
   :alt: Redshift and mass distributions M*≥10.24

   Redshift (left) and stellar-mass (right) distributions for the M★≥10.24 mock.
   Density is matched to within 0.001% of the observed value.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.24_Mstar_12.0_0.05_z_0.18_N_0781950_compare_zMstar.png
   :width: 90%
   :alt: z-M* plane M*≥10.24

   Stellar-mass vs. redshift plane for the M★≥10.24 mock and the corresponding BGS sample.

M★ ≥ 10.45 (N = 936 461, z < 0.22)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.45_Mstar_12.0_0.05_z_0.22_N_0936461_compare_sky.png
   :width: 90%
   :alt: Sky footprint of mock M*≥10.45

   Sky footprint (RA/Dec) of the M★≥10.45 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.45_Mstar_12.0_0.05_z_0.22_N_0936461_compare_1D.png
   :width: 90%
   :alt: Redshift and mass distributions M*≥10.45

   Redshift (left) and stellar-mass (right) distributions for the M★≥10.45 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.45_Mstar_12.0_0.05_z_0.22_N_0936461_compare_zMstar.png
   :width: 90%
   :alt: z-M* plane M*≥10.45

   Stellar-mass vs. redshift plane for the M★≥10.45 mock and the corresponding BGS sample.

M★ ≥ 10.65 (N = 923 373, z < 0.26)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.65_Mstar_12.0_0.05_z_0.26_N_0923373_compare_sky.png
   :width: 90%
   :alt: Sky footprint of mock M*≥10.65

   Sky footprint (RA/Dec) of the M★≥10.65 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.65_Mstar_12.0_0.05_z_0.26_N_0923373_compare_1D.png
   :width: 90%
   :alt: Redshift and mass distributions M*≥10.65

   Redshift (left) and stellar-mass (right) distributions for the M★≥10.65 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.65_Mstar_12.0_0.05_z_0.26_N_0923373_compare_zMstar.png
   :width: 90%
   :alt: z-M* plane M*≥10.65

   Stellar-mass vs. redshift plane for the M★≥10.65 mock and the corresponding BGS sample.

M★ ≥ 10.84 (N = 793 669, z < 0.31)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.84_Mstar_12.0_0.05_z_0.31_N_0793669_compare_sky.png
   :width: 90%
   :alt: Sky footprint of mock M*≥10.84

   Sky footprint (RA/Dec) of the M★≥10.84 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.84_Mstar_12.0_0.05_z_0.31_N_0793669_compare_1D.png
   :width: 90%
   :alt: Redshift and mass distributions M*≥10.84

   Redshift (left) and stellar-mass (right) distributions for the M★≥10.84 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_10.84_Mstar_12.0_0.05_z_0.31_N_0793669_compare_zMstar.png
   :width: 90%
   :alt: z-M* plane M*≥10.84

   Stellar-mass vs. redshift plane for the M★≥10.84 mock and the corresponding BGS sample.

M★ ≥ 11.03 (N = 460 808, z < 0.35)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. figure:: ../figures/runs/MOCK_VLIM_ANY_11.03_Mstar_12.0_0.05_z_0.35_N_0460808_compare_sky.png
   :width: 90%
   :alt: Sky footprint of mock M*≥11.03

   Sky footprint (RA/Dec) of the M★≥11.03 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_11.03_Mstar_12.0_0.05_z_0.35_N_0460808_compare_1D.png
   :width: 90%
   :alt: Redshift and mass distributions M*≥11.03

   Redshift (left) and stellar-mass (right) distributions for the M★≥11.03 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_11.03_Mstar_12.0_0.05_z_0.35_N_0460808_compare_zMstar.png
   :width: 90%
   :alt: z-M* plane M*≥11.03

   Stellar-mass vs. redshift plane for the M★≥11.03 mock and the corresponding BGS sample.

M★ ≥ 11.22 (N = 157 946, z < 0.35)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. figure:: ../figures/runs/MOCK_VLIM_ANY_11.22_Mstar_12.0_0.05_z_0.35_N_0157946_compare_sky.png
   :width: 90%
   :alt: Sky footprint of mock M*≥11.22

   Sky footprint (RA/Dec) of the M★≥11.22 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_11.22_Mstar_12.0_0.05_z_0.35_N_0157946_compare_1D.png
   :width: 90%
   :alt: Redshift and mass distributions M*≥11.22

   Redshift (left) and stellar-mass (right) distributions for the M★≥11.22 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_11.22_Mstar_12.0_0.05_z_0.35_N_0157946_compare_zMstar.png
   :width: 90%
   :alt: z-M* plane M*≥11.22

   Stellar-mass vs. redshift plane for the M★≥11.22 mock and the corresponding BGS sample.

M★ ≥ 11.39 (N = 50 067, z < 0.35)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. figure:: ../figures/runs/MOCK_VLIM_ANY_11.39_Mstar_12.0_0.05_z_0.35_N_0050067_compare_sky.png
   :width: 90%
   :alt: Sky footprint of mock M*≥11.39

   Sky footprint (RA/Dec) of the M★≥11.39 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_11.39_Mstar_12.0_0.05_z_0.35_N_0050067_compare_1D.png
   :width: 90%
   :alt: Redshift and mass distributions M*≥11.39

   Redshift (left) and stellar-mass (right) distributions for the M★≥11.39 mock.

.. figure:: ../figures/runs/MOCK_VLIM_ANY_11.39_Mstar_12.0_0.05_z_0.35_N_0050067_compare_zMstar.png
   :width: 90%
   :alt: z-M* plane M*≥11.39

   Stellar-mass vs. redshift plane for the M★≥11.39 mock and the corresponding BGS sample.

Stellar mass function
---------------------

.. figure:: ../figures/runs/mock_smf_overlay.png
   :width: 90%
   :alt: Mock SMF overlay

   Stellar mass function φ(M★) for all 9 Uchuu mock VLIM samples,
   estimated with the 1/Vmax method (coloured markers with jackknife errors).
   The cosmological area (5 156.6 deg²) is used for normalisation.
   Literature references overlaid as dashed/dotted lines:
   Baldry+2012 GAMA I, Driver+2022 GAMA DR4, Moustakas+2013 PRIMUS z<0.2,
   Xu+2025 DESI PAC (shaded band).
   See :ref:`literature` for provenance.

SMF key values at the lowest complete stellar mass bin:

.. list-table::
   :header-rows: 1
   :widths: 30 10 12 22 22

   * - Sample
     - log₁₀M★_min
     - z_max
     - log₁₀M★_ref [dex]
     - φ [Mpc⁻³ dex⁻¹]
   * - MOCK_VLIM_ANY_Mstar9.29
     - 9.29
     - 0.08
     - 9.38
     - 7.00 × 10⁻³ ± 1.6 × 10⁻⁴
   * - MOCK_VLIM_ANY_Mstar9.78
     - 9.78
     - 0.12
     - 9.88
     - 5.53 × 10⁻³ ± 9.2 × 10⁻⁵
   * - MOCK_VLIM_ANY_Mstar10.24
     - 10.24
     - 0.18
     - 10.12
     - 1.92 × 10⁻⁴ ± 2.9 × 10⁻⁶
   * - MOCK_VLIM_ANY_Mstar10.45
     - 10.45
     - 0.22
     - 10.38
     - 8.67 × 10⁻⁴ ± 1.1 × 10⁻⁵
   * - MOCK_VLIM_ANY_Mstar10.65
     - 10.65
     - 0.26
     - 10.62
     - 1.56 × 10⁻³ ± 1.6 × 10⁻⁵
   * - MOCK_VLIM_ANY_Mstar10.84
     - 10.84
     - 0.31
     - 10.88
     - 1.51 × 10⁻³ ± 1.3 × 10⁻⁵
   * - MOCK_VLIM_ANY_Mstar11.03
     - 11.03
     - 0.35
     - 11.12
     - 8.84 × 10⁻⁴ ± 9.2 × 10⁻⁶
   * - MOCK_VLIM_ANY_Mstar11.22
     - 11.22
     - 0.35
     - 11.12
     - 7.88 × 10⁻⁵ ± 8.9 × 10⁻⁷
   * - MOCK_VLIM_ANY_Mstar11.39
     - 11.39
     - 0.35
     - 11.38
     - 7.38 × 10⁻⁵ ± 9.2 × 10⁻⁷

Angular correlation function w(θ)
----------------------------------

.. figure:: ../figures/runs/mock_wtheta_overlay.png
   :width: 90%
   :alt: Mock w(theta) overlay

   Angular two-point correlation function w(θ) for all 9 mock samples,
   measured with the Landy–Szalay estimator.  Error bars are TreeCorr
   variance estimates.  Bins: 30 log-spaced bins in [0.01, 60] arcmin.

Projected correlation function w\ :sub:`p`\ (r\ :sub:`p`)
-----------------------------------------------------------

.. figure:: ../figures/runs/mock_wp_overlay.png
   :width: 90%
   :alt: Mock wp overlay

   Projected correlation function w\ :sub:`p`\ (r\ :sub:`p`) for all 9 mock
   samples (π\ :sub:`max` = 100 Mpc), measured with Corrfunc Landy–Szalay.
   Error bars are jackknife uncertainties from the joint covariance.
   Bins: 30 log-spaced bins in [0.01, 60] Mpc.

Representative w\ :sub:`p`\ (r\ :sub:`p`) values at r\ :sub:`p` = 1 Mpc and 10 Mpc
(from the joint covariance files, uniform weights):

.. list-table::
   :header-rows: 1
   :widths: 35 10 22 22

   * - Sample
     - log₁₀M★_min
     - w\ :sub:`p`\ (1 Mpc) [Mpc]
     - w\ :sub:`p`\ (10 Mpc) [Mpc]
   * - MOCK_VLIM_ANY_Mstar9.29
     - 9.29
     - 164.8 ± 20.5
     - 19.0 ± 14.1
   * - MOCK_VLIM_ANY_Mstar9.78
     - 9.78
     - 201.4 ± 15.7
     - 26.4 ± 11.8
   * - MOCK_VLIM_ANY_Mstar10.24
     - 10.24
     - 222.6 ± 10.5
     - 29.6 ± 7.8
   * - MOCK_VLIM_ANY_Mstar10.45
     - 10.45
     - 238.6 ± 8.4
     - 32.9 ± 7.3
   * - MOCK_VLIM_ANY_Mstar10.65
     - 10.65
     - 255.1 ± 7.2
     - 34.5 ± 5.2
   * - MOCK_VLIM_ANY_Mstar10.84
     - 10.84
     - 274.8 ± 8.3
     - 36.5 ± 6.7
   * - MOCK_VLIM_ANY_Mstar11.03
     - 11.03
     - 317.4 ± 6.8
     - 40.7 ± 3.9
   * - MOCK_VLIM_ANY_Mstar11.22
     - 11.22
     - 395.7 ± 11.8
     - 49.5 ± 4.4
   * - MOCK_VLIM_ANY_Mstar11.39
     - 11.39
     - 571.4 ± 40.7
     - 65.1 ± 6.6

Joint SMF + w\ :sub:`p` covariance
------------------------------------

The joint covariance matrix is estimated with 100-region spatial jackknife
resampling.  The data vector is
:math:`\mathbf{d} = [\phi_1,\ldots,\phi_{N_\mathrm{SMF}},\, w_p^1,\ldots,w_p^{N_{w_p}}]`.

.. figure:: ../figures/runs/mock_joint_corrmat.png
   :width: 100%
   :alt: Mock joint correlation matrices

   Pearson correlation matrices of the joint SMF + w\ :sub:`p` data vector
   for all 9 mock samples.  The dashed line separates the SMF (top-left)
   from the w\ :sub:`p` (bottom-right) blocks.  Off-diagonal cross-correlations
   encode the covariance between the two statistics.

Regenerating figures
---------------------

After new results are available, re-run::

    python docs/scripts/make_run_figures.py
    cd docs && make html